PostGIS sfcgal ST_3DArea

Question

I want to compute surface areas of a large CityGML data set. However, I ran into some issues, which I could not resolve or fully understand.

The error message is the following:

Polygon is invalid : points don't lie in the same plane

Minimal examples:

1. SELECT st_3darea( ST_SetSrid(ST_GeometryFromText( 'POLYGON Z ((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0))' ),4258)) /*<- This works fine */

2. SELECT st_3darea( ST_SetSrid(ST_GeometryFromText( 'POLYGON Z ((0 0 0, 0 11, 1 1 0, 1 0 0, 0 0 0))' ),4258)) /*<- This does not work: Error Polygon is invalid : points don't lie in the same plane */

3. SELECT st_3darea( ST_SetSrid(ST_GeometryFromText( 'POLYGON Z ((0 0 0, 0 11, 1 11, 1 0 0, 0 0 0))' ),4258)) /*<- This works fine again */

4. SELECT st_3darea( ST_SetSrid(ST_GeometryFromText( 'POLYGON Z ((0 0 0, 0 1 1, 1 0 0, 0 0 0))' ),4258)) /*<- This works fine, removed one point */

From my understanding in 2), the function is not able to transform the coordinates into a flat plane to proceed with its calculations. Somehow, I am not sure if it is a bug or a feature (is the polygons in 2) invalid, why?)

As answered by@geozelot, its not a bug, but PostGIS does not support curved geometries.

My idea for a solution:

Is there a generic workflow/function to split polygons (e.g. 2)) in a form like in 4) triangles and then add the sums of the areas?

I would need it automated for the CityGML data set, which I do not know how to do e.g. non-automated

SELECT st_3darea( ST_SetSrid(ST_GeometryFromText( 'POLYGON Z ((0 0 0, 0 1 1, 1 0 0, 0 0 0))' ),4258)) + SELECT st_3darea( ST_SetSrid(ST_GeometryFromText( 'POLYGON Z ((0 1 1, 1 1 1, 1 0 0, 0 1 1))' ),4258))

Answer 1

The vertices given in 2) cannot be elements of the same 2-dimensional plane; i.e. vertex (0 1 1) cannot be contained in the plane defined by the other vertices. Simple POLYGON geometries (or faces), no matter the Z component, must not be curved.

PostGIS does have (limited) support for CURVED geometries that could be used for non-linear faces, e.g.

SELECT ST_AsText(ST_SetSrid(ST_GeometryFromText( 'CURVEPOLYGON(CIRCULARSTRING(0 0 0, 0 1 1, 1 1 0, 1 0 0, 0 0 0))' ),4258));

however, they won't solve your issue.

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Note that ST_IsValid won't detect this as it does not consider z values; ST_IsPlanar, however, should detect this.